1. Field of the Invention
The present invention relates to digital to analog converters (DACs) for audio frequencies. More particularly, this invention relates to correction of nonlinear output distortion in delta sigma DACs.
2. Description of the Prior Art
Delta sigma modulation incorporates a noise-shaping technique whereby the noise of a quantizer (often 1-bit) operating at a frequency much greater than the bandwidth is moved to frequencies not of interest in the output signal. A filter after the quantizer removes the out of band noise. The resulting system synthesizes a high resolution data converter, but is constructed from low resolution building blocks. A good overview of the theory of delta sigma modulation is given in "Oversampling Delta-Sigma Data Converters," by Candy and Temes, IEEE Press, 1992.
FIG. 1 shows a well known first order delta sigma quantizer. The purpose of this quantizer, in a digital to analog (D/A) converter, is to convert a high resolution digital signal xi, 11, having several bits (16 for example) into a single-bit code yi, 12, which can be accurately converted to analog. Input 11 is fed to the quantizer via an integrator 16, and quantized output 12 is fed back as feedback 25 and subtracted using adder 14 from the input. Integrator 16 comprises delay 18, and adder 17, which adds the delayed signal 19 to the signal from adder 14. Quantizer 21 acts as a 1-bit A/D converter, driving its output to a negative one (given a negative input) or a positive one (given a positive input). The quantizer function is modeled as adding the output of integrator 16 to an error signal ei, 23. This modeling allows the calculation of the spectrum of the noise to be done in a straight forward manner.
For large positive inputs, the integrator output will be positive. A logic one is then the output of the quantizer, which is fed back and subtracted from the input. The series of output ones continues until the integrator output , which is ramping down due to the negative feedback, finally crosses the quantizer threshold, when the quantizer outputs a negative one. Over time, the average output yi equals the input xi. The system is called a first order delta sigma converter, because a single integrator stage is used.
FIG. 2 shows how output yi, 31, looks for a sinusoidal input xi, 30. When the input sine wave is at a high level, a large number of ones are generated. When the input sine wave is at a low level, a large number of negative ones are generated.
FIG. 3 shows a common second order delta sigma quantizer. In practice, delta sigma modulators are generally at least second order, because higher order modulators better reduce noise in the signal band, due to improved prediction of the in-band quantization error. Thus, the resulting signal to noise ratio is better. Second order delta sigma modulators are still relatively stable, and easy to design.
Input xi, 35, is added to feedback signal 54 by adder 38. The signal from adder 38 is fed into first accumulator 40, comprising delay 42 and adder 41. The output of accumulator 40 is added to feedback signal 54 and fed into second accumulator 44, comprising delay 47 and adder 45. The output of accumulator 44 goes into quantizer 50, modeled as error signal ei, 52, added to the input by adder 51. Quantized output 36 also feeds back as feedback signal 54. Quantizer 50 may quantize the signal into ones and zeroes (1-bit format) or into multiple levels.
FIG. 4 shows an oversampling digital to analog (D/A) converter, which utilizes a second order delta sigma quantizer 70 and a one-bit D/A converter 71 as the demodulator 69, and a low pass filter 73 to remove the noise from the 1-bit signal. In one specific example of the oversampling D/A converter of FIG. 4, the input signal xi, 60, consists of data encoded into 16 bit words at 8 kHz. These words are placed into a register 63 from which they are fed into a low pass filter 64 at 32 kHz, with each word repeated four times. The low pass filter would typically by of the finite impulse response type. The linear interpolator 66, which is also a low pass filter, inserts three new words between each pair of words from low pass filter 64, which raises the data rate to 128 kHz. These words are fed into a second register 67, which feeds each word into the demodulator 69, repeating each word eight times, resulting in a data rate of 1 MHz. This repeating of the samples is a simple type of low pass filter. The 1 MHz sample rate is a sufficiently high data rate so that the quantization noise which will be introduced into the signal is small, and the requirements of the analog smoothing filter are easily met. Output yi, 61, is an analog signal.
Techniques for increasing the sample rate, generally called interpolation, are well understood by those versed in the art. Most designs will utilize several stages of increase, with each successive stage being simpler in structure, and running at a faster rate.
This sort of demodulator is frequently used in audio applications. The output of demodulator 69 can sometimes be driven directly into a speaker (not shown), because the speaker can act as a low pass filter. This configuration uses what is called class D output. Power dissipation in a class D stage has the potential for being very low, as the output transistors are always in either a fully shorted or open position, removing most resistive power consumption. The remaining power is dissipated by the switching of capacitance, which is equal to C*V.sup.2 *F. C, the capacitance being switched, is typically set by the parasitic capacitance of the output transducer and of the driver transistors. V, the voltage being switched, is set by the available supplies, and the required audio output. F, the average frequency of the output, can be varied by the designer. As F is made larger, the quality of the signal improves, but the power also increases. Also the calculations themselves require power dissipation.
An over-sampling digital to analog (D/A) converter like that of FIG. 4, which utilizes a second order delta sigma quantizer 70, and a low pass filter 71 to convert the data from the delta sigma quantizer 70 to analog signal yi, 61, is a very effective device. However, it has a relatively high output data transition rate, requiring higher power than is desirable. The use of a pulse width modulator to convert the high resolution, low rate data into a low resolution, high rate output signal reduces the transition rate, but introduces nonlinear distortion into the output signal, reducing its accuracy.
European patent EP 0576 701 B1 shows a hearing aid having an A/D converter to convert the input sound to a digital format, conventional digital signal processing, and a pulse width modulator to convert the high resolution, low rate data into a low resolution, high rate class D output, meaning the digital bit stream drives an output transducer directly. The output of the pulse width modulator has relatively low transition rates, but since there is no noise shaping in the circuit, it has a low signal to noise ratio. An extremely high clock rate would be required to achieve good audio fidelity.
Other systemic nonlinear effects may be introduced into the output signal by the output 1-bit or multilevel DAC or other parts of the output system. It is well understood that a delta sigma converter can be partially corrected for feedback non-linearity by introduction of a non linear element driving all of the feedback paths. There are many kinds of output distortions that cannot be corrected by this means. A need remains in the art for a D/A converter capable of compensating for nonlinear output distortion caused by predictable systemic factors that the single element cannot correct.